Lawyers aren't shy of reminding the world of their unique constitutional status. Listening to these noble upholders of the rule of law reflect on their position at the heart of modern democracy, you'd be forgiven for assuming they had been carefully selected from a broad cross section of society.

The reality, though, is depressingly different: a survey last month found that lawyers are more than seven times as likely to have been privately educated than members of the general population.

Remedying this situation is one of the main aims of the impending review of legal education. Another is doing something about the serious mismatch between numbers of law students and trainee lawyer jobs. Last year more than 7,000 prospective solicitors enrolled on the year-long legal practice course — which costs up to £12,500 — but there were only 4,510 training contracts available at the end of it. The situation is even worse at the bar, with around 4,000 bar professional training course (BPTC) graduates routinely fighting it out for just 500 pupillages.

Many believe the answer to these problems is an aptitude test to filter out those unlikely to secure traineeships before they embark on legal professional skills courses. They argue that such a move would resolve issues of over-supply and give successful students from low-income backgrounds greater confidence to take out loans to cover their fees.

But competition law could scupper this idea. An attempt by the barristers' regulator, the Bar Standards Board, to introduce an aptitude test last year for entry on to the BPTC was blocked by the Office of Fair Trading on the grounds that it would ultimately lead to "decreased quality and availability and increased prices in the final market for advocacy services."

And even if these concerns were overcome, there are doubts about how effective an aptitude test would really be at encouraging students from less wealthy families to enter law – especially in view of the coalition's undergraduate fee increases and the associated incentive to keep costly higher education to a minimum.

If the legal profession is serious about changing its make up, it needs to do something more radical. One idea that stands out is the apprenticeship-style approach mooted last month by Legal Services Board chairman David Edmonds, which would see some of the professional training responsibilities that currently reside with the law schools reallocated to law firms and barristers' chambers. This would cut costs for prospective lawyers, who could study while they worked without getting into more debt.

The timing looks right for this kind of model. With the legal profession more fragmented than ever – high street solicitors and international corporate lawyers would be the first to admit that they don't have much in common – law firms are increasingly open to the possibility of professional legal training being conducted in-house on a more specialist basis, even if that means picking up more of the cost themselves. Meanwhile, law schools, which would have the most to lose if an apprenticeship model were introduced, are seen by many in the profession as in need of being reined in.

The relentless focus on profit of these mostly private institutions was illustrated by the recent decision of BPP Law School to open three new branches in spite of the current surplus of law graduates. And its rival, the College of Law, a registered charity, did itself no favours with its decision last year to pay chief executive Nigel Savage £440,000 (more than the vice-chancellor of every British university except the London Business School, and at least double what the bosses of most other UK-based charities earn).

The legal regulators conducting the education review have a choice: they can tinker with a dysfunctional system that runs contrary to the core values of the profession it serves, or they can overhaul it. Let's see what option they take.